Interactions of type IIB D-branes from D-instanton matrix model

TL;DR

The work analyzes long-range interactions between type IIB D-brane bound states within the IKKT (type IIB matrix) framework and demonstrates exact agreement with classical supergravity in the large-$N$ limit. By computing potentials on the closed-string side via probe methods and on the open-string side via one-loop matrix-model SYM with D-instanton backgrounds, the authors reveal that D-branes are effectively populated by a large number of D-instantons, encoding non-marginal bound-state physics through $F^4$ (and higher) invariants. The results establish a concrete mapping between matrix-model backgrounds with constant flux and non-abelian Born-Infeld-type terms, clarifying how $F^4$ structures arise in the SYM effective action and reproduce the corresponding supergravity interactions. The analysis relies on T-duality to relate D-instanton configurations to Dp-branes and connects to BFSS-type results, reinforcing the matrix model as a nonperturbative description of D-brane dynamics in type IIB string theory.

Abstract

We compute long-distance interaction potentials between certain 1/2 and 1/4 supersymmetric D-brane configurations of type IIB theory, demonstrating detailed agreement between classical supergravity and one-loop instanton matrix model results. This confirms the interpretation of D-branes as described by classical matrix model backgrounds as being `populated' by large number of D-instantons, i.e. as corresponding to non-marginal bound states of branes of lower dimensions. In the process, we establish precise relation between matrix model expressions and non-abelian F^4 terms in the super Yang-Mills effective action.